Editing Arbitrated Quantum Digital Signature (section)

==Outline==

Like other QDS protocols, it is divided into two phases: Distribution and Messaging. This scheme is presented between the seller (one who signs the message), the buyer (one whom the signed message is sent) and PKG (generates and distributes public-private key for the seller) and a buyer. </br> Distribution includes the generation of public and private keys as follows 
* '''Key Generation''': In this step, PKG generates the public key of the seller and generates a private key which is secretly sent to Seller over the insecure classical channel. 
**Seller's public key is derived from her personal information such as her email-id over a public channel. A one-way function is chosen by PKG randomly and secretly (known as the master key), which uses the classical public key as its input. 
**A random OTP of the same length as the outcome of the function (random key), is used to convert it (the outcome) into seller's private key by performing bit-wise modulo 2 sum (exclusive OR gate). 
**The quantum pre-shared common key (assumption) is then used to one-time pad the private key via [[Arbitrated Quantum Digital Signature#References|Quantum Vernam Cipher (1), (2)]]. The one-time padded cipher-text is then communicated to the seller (over the insecure channel). 
**Seller un-pads the cipher-text to obtain the private key using the pre-shared common key. Hence, in the end, everyone knows the seller's public key and, only PKG and seller know her private key. 
Messaging comprises of the following steps
* '''Signing''': In this step, the seller generates a signature quantum state using the message she wants to send, her public key and private key. The seller selects a quantum one-way function publicly to generate a quantum digest (directory) using these classical inputs. Seller repeats each step for each message bit.
** Seller selects two random strings and generates a quantum state of the message using these random strings to operate a Unitary gate and [[Glossary#Quantum Gates|Hadamard Transform]] on a null/vacuum state (see [[Arbitrated Quantum Digital Signature#Pseudo Code|Pseudo Code]] for operations)
** The public and the private key are used to perform Hadamard transformation on the state produced in the previous step in order to generate the signature quantum state.
** The Seller then performs some operation using her private key and measures the quantum state. It can be shown the states were one of the BB84 states and hence, can have one of the two possible bases ([[Glossary#Quantum States|X basis, Z basis or + basis,x basis]]) and four possible states. She records the basis and classical bit representing the state obtained. 
**Seller then concatenates these classical bits, the two random string bits, and a timestamp unique to the signature. The concatenated classical string is used as the input of publicly chosen QOWF, to get the output called 'quantum digest'. She produces some copies of quantum digest for each recipient (buyer).  
**Seller then encrypts the timestamp and quantum output of QOWF with pre-shared common key via quantum vernam cipher. PKG unpads these and publicly announces for buyer's verification step. 
** Sellers sends the signature to the buyer which includes the signature quantum state, message, timestamp and basis states.

* '''Verification''': In this method, buyer checks the authenticity of the signature (whether the message has come from a genuine seller).
** The buyer performs some quantum gates on the signature quantum state, using seller's public key and message. He measures the resulting quantum state, using basis states for each qubit sent in the signature. The result thus, obtained is represnted by a classical string, in the same way as done by seller.
**The result should reveal the random string used by seller and hence, buyer can also generate the same number of copies of the quantum digest using the publicly known QOWF.
**Buyer, thus, compares his outputs of QOWF with the ones sent by the seller using [[Glossary#SWAP test|quantum SWAP Test]]. If the number of matches is greater than the accepted/decided threshold value, the signature is accepted else it is rejected.